CRITICAL POINT THEOREMS AND APPLICATIONS

Critical Point Theorems for Nonlinear Dynamical Systems and Their Applications

We present some new critical point theorems for nonlinear dynamical systems which are generalizations of Dancš-Hegedüs-Medvegyev’s principle in uniform spaces and metric spaces by applying an abstract maximal element principle established by Lin and Du. We establish some generalizations of Ekeland’s variational principle, Caristi’s common fixed point theorem for multivalued maps, Takahashi’s no...

Critical Point Theorems and Ekeland Type Variational Principle with Applications

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...

Fixed Point Theorems and Applications

Quantitative Deformation Theorems and Critical Point Theory

It is well known that deformation theorems are the basic tools in critical point theory. They can be derived under a condition of Palais-Smale type ((PS), for short). In the classical setting of a C1 functional f defined on a Banach space X (or a C2 Finsler manifold), we refer to [15]; for a continuous functional f defined on a complete metric space X, we refer to [8], the results of which incl...

Krasnoselskii Type Fixed Point Theorems and Applications

In this paper, we establish two fixed point theorems of Krasnoselskii type for the sum of A + B, where A is a compact operator and I − B may not be injective. Our results extend previous ones. As an application, we apply such results to obtain some existence results of periodic solutions for delay integral equations and then give three instructive examples.